Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Make 24

Date: 01/03/2003 at 06:01:51
From: Hasan
Subject: Make 24 using 1,3,4,6

We have to make 24 by using 1, 3, 4, and 6. We can use +,-,*,/. 
What is the answer? Is it (14-6) * 3 = 24?

Date: 01/03/2003 at 13:01:33
From: Doctor Ian
Subject: Re: Make 24 using 1,3,4,6

Hi Hasan,

That certainly looks like an answer, assuming you can place digits
together as you've done (i.e., making '14' from '1' and '4'). You'd
have to check with your teacher to see if it's considered 'legal'.  

Note that if you can use exponents, an answer would be

  1  * 4 * 6

However, there's a sneaky way to get what amounts to a fifth number,
by doing this:

  24 = -------
        b - -

  24 = --------
        bd   c
        -- - -           Get a common denominator
         d   d

  24 = --------
        bd - c
        ------           Subtract

  24 = --------          Invert and multiply
        bd - c

Now, this is a little simpler, because we need to get a multiple of 24
on top, and something on the bottom that will reduce it back to 24. 

The obvious way to do that would be to get 24 on top, and 1 on the 

  24 = --------          Invert and multiply
        b*4 - c
Can you get the denominator to be equal to 1, using 1 and 3 as 
possible values for b and c? 

- Doctor Ian, The Math Forum
Associated Topics:
High School Puzzles
Middle School Puzzles

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.